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大会报告
大会科普
丁龙云 (南开大学) | 等价关系与波莱尔归约
摘要：近年来，在描述集合论中，数理逻辑学家们发展出了一个非常有用的工具——波莱尔归约，用于刻画在数学的各个分支里受到关注的等价关系和分类问题之间的相对的复杂程度。在本次报告中，我们将就这一主题，从它的起源到发展现状，做一个综述。
分会场
递归论：
方楠 (中国科学院) | Speedability of computably approximable reals and their approximations
Abstract. An approximation of a real is a sequence of rational numbers that converges to the real. An approximation is left-c.e. if it is computable and nondecreasing and is d.c.e. if it is computable and has bounded variation. A real is computably approximable if it has some computable approximation, and left-c.e. and d.c.e. reals are defined accordingly. An approximation ${a_s}_{s in omega}$ is emph{speedable} if there exists a nondecreasing computable function $f$ such that the approximation ${a_{f(s)}}_{s in omega}$ converges in a certain formal sense faster than ${a_s}_{s in omega}$. This leads to various notions of speedability for reals, e.g., one may require for a computably approximable real that either all or some of its approximations of a specific type are speedable. Merkle and Titov established the equivalence of several speedability notions for left-c.e. reals that are defined in terms of left-c.e. approximations. We extend these results to d.c.e. reals and d.c.e. approximations, and we prove that in this setting, being speedable is equivalent to not being Martin-L”{o}f random. Finally, we demonstrate that every computably approximable real has a computable approximation that is speedable. This is joint work with George Barmpalias, Wolfgang Merkle, and Ivan Titov.
吴慧珊 (北京语言大学) | The complexity of computable semisimple rings
Abstract. The theory of semisimple rings plays a fundamental role in noncommutative algebra. We study the complexity of the problem of semisimple rings by the index set method in computable structure theory. We define a computably enumerable ring as the quotient ring of a computable ring modulo a computably enumerable congruence relation and view such rings as structures in the language of rings, together with a binary relation. We prove that the index set of computably enumerable semisimple rings is Σ^0_3-complete. However, the corresponding results on computable semisimple rings are different. Recently, we develop a new d-Σ^0_2 definition for semisimple rings and prove that the index set of computable semisimple rings is d-Σ^0_2-complete. This is a recent joint work with Jake Rhody.
模型论：
Leo Jimenez (俄亥俄州大学) | Domination and semi-minimal analysis in superstable theories
Abstract. In model theory, the notion of type is of central importance, as completely encoding the properties of some elements in a model. In specific finite-dimensional theories, called superstable, there are two ways to decompose types: domination-equivalence to a product of minimal types, or using a sequence of fibrations, where each fiber is semiminimal. In this talk, I will define these words and explain the connections between these two decompositions. Along the way, I will use differential equations to provide guiding examples, and conclude with an application to Lotka-Volterra systems. This is joint work with Christine Eagles and Yutong Duan.
集合论：
戴威 (南开大学) | Isometry groups and countable groups with the L’evy propertyess
Abstract. In the study of extremely amenable groups, the L’evy property, also known as the concentration of measure phenomenon, plays an important role. The L’evy property implies extremely amenability, and historically, many well-known groups are shown to be extremely amenable by proving that they have the L’evy property. In this talk, I will present some new classes of isometry groups and countable groups with the L’evy property. As a consequence, we show that there are at least continuum many pairwise non-isomorphic separable metrizable groups with the L’evy property. Moreover, for any given countable locally finite omnigenous group $H$, we can choose a L’evy sequence such that its increasing union is isomorphic to $H$. If time is permitted, we will also discuss some analogous results in continuous logic and mention some open questions. This is joint work with Su Gao and V’ıctor Hugo Ya~nez.
申国桢 (中山大学-珠海) | Amorphous sets and dual Dedekind finiteness
Abstract. A set $A$ is dually Dedekind finite if every surjection from $A$ onto $A$ is injective; otherwise, $A$ is dually Dedekind infinite. An amorphous set is an infinite set that cannot be partitioned into two infinite subsets. A strictly amorphous set is an amorphous set in which every partition has only finitely many non-singleton blocks. It is proved consistent with $mathsf{ZF}$ (i.e., Zermelo–Fraenkel set theory without the axiom of choice) that there exists an amorphous set $A$ whose power set $mathscr{P}(A)$ is dually Dedekind infinite, which gives a negative solution to a question proposed by Truss [J. Truss, emph{Fund. Math.} 84, 187–208 (1974)]. Nevertheless, we prove in $mathsf{ZF}$ that, for all strictly amorphous sets $A$ and all natural numbers $n$, $mathscr{P}(A)^n$ is dually Dedekind finite, which generalizes a result of Goldstern. This is joint work with Yifan Hu and Ruihuan Mao.
哲学逻辑：
马明辉 (中山大学) | The Lattice of Inflationary Superintuitionistic Logics
Abstract. Inflationary intuitionistic logic extends intuitionistic propositional logic with an inflationary modal operator $Box$. We first introduce both the Kripke semantics and algebraic semantics for this logic, then establish the Stone-style representation theory for inflationary Heyting algebras, which yields some Goldblatt-Thomason theorems. Further, we present the lattice of inflationary superintuitionistic logics. We will give a series of results on finite approximability and local tabularity by algebraic methods; notably all finite depth logics are locally tabular. Finally, we characterize splitting logics in the lattice as those axiomatized by Jankov-style formulas for finite subdirectly irreducible inflationary Heyting algebras.
谢凯博 (武汉大学) | A Logical Analysis of Two Interpretations of Nested Counterfactuals
Abstract. Both causal Bayesian networks (CBNs) and structural causal models (SCMs) can be used to analyze the possibility of counterfactual conditionals: within a certain scope, their predictions regarding the probability distribution under counterfactual assumptions are identical. However, conceptually, the two approaches diverge: CBNs first excute interventions and then calculate probability distributions based on the updated graph, whereas SCMs evaluate the truth of counterfactual conditionals relative to each possible world separately, and subsequently aggregating the probabilities of the worlds that satisfy the statement—a philosophical perspective known as the “Laplacian” interpretation. This talk will analyze the differences between the two interpretations from the perspective of the nesting of modal operators and investigate their logical properties.
熊作军 (西南大学) | 秘密逻辑与秘密推理
Abstract. 报告将以“秘密”与“知识”的理解为切入口，将秘密看作是初始模态算子，分析讨论其对应的逻辑系统。进一步梳理近年来“秘密逻辑”方面的研究进展与主要结果，讨论秘密动态化、推理的保密性、群体秘密等相关扩展研究。